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  4. If cot- 1((n/2 π ))>(2 π /3) , then the maximum value of the integer n is

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Q. If $cot^{- 1}\left(\frac{n}{2 \pi }\right)>\frac{2 \pi }{3}$ , then the maximum value of the integer $n$ is

NTA AbhyasNTA Abhyas 2020Inverse Trigonometric Functions

Solution:

We have, $\frac{2 \pi }{3} < cot^{- 1}\left(\frac{n}{2 \pi }\right) < \pi \Rightarrow cot\frac{2 \pi }{3}>\frac{n}{2 \pi }>-\in fty$
$\Rightarrow -\frac{1}{\sqrt{3}}>\frac{n}{2 \pi }>-\in fty\Rightarrow -\frac{2 \pi }{\sqrt{3}}>n>-\in fty$
Maximum value of $n$ is $-4$